NCERT Solutions Class 6 Maths Chapter 9 Symmetry Exercise 9.1

Exercise 9.1 of the NCERT Solutions for Class 6 Maths in Chapter 9 (Symmetry) is a wonderful way to introduce students to the world of symmetrical figures. The exercise is designed to help students recognize symmetry and interpret it in terms of everyday objects and shapes. The exercise focuses on line symmetry also known as reflectional symmetry; where a figure can be folded along the line so that the two halves would coincide perfectly.  

Once students are confident in locating lines of symmetry during this exercise, they will have a strong visual and conceptual foundation for symmetrical patterns and transformations in higher classes.

1.0Download NCERT Solutions of Class 6 Maths Chapter 9 Symmetry Exercise 9.1

Download for free NCERT Solutions for Class 6 Maths Chapter 9, Symmetry, Exercise 9.1, to learn line symmetry.

Key Concepts of Exercise 9.1

• Symmetry: the state or quality of an object or figure that will perform in the same physical way when subject to a given action, such as reflection and rotation. 
• Line Symmetry (Reflectional Symmetry): A figure has line symmetry when it can be folded along a given line for one part of the figure will in fact coincide precisely with each other .
• Line of Symmetry (Axis of Symmetry): The imaginary (or real) line that a figure can be folded along, to create two halves that are symmetrical.
• Finding Lines of Symmetry: Practicing finding one or more lines of symmetry in different two-dimensional shapes of square, rectangle, triangle, circle, letters of the alphabet, and other shapes seen around the students.
• Symmetrical Figures: What is a symmetrical figure? A symmetrical figure has at least one line of symmetry.

2.0NCERT Exercise Solutions Class 6 Chapter 9 Symmetry : All Exercises 

3.0NCERT Class 6 Maths Chapter 9 Symmetry Exercise 9.1 : Detailed Solutions

9.1 Line of Symmetry

1. Do you see any line of symmetry in the figures at the start of the chapter? What about in the picture of the cloud? Sol. The butterfly, flower, pinwheel, and rangoli at the start of the chapter exhibit symmetry.
   
   The cloud does not have symmetry as it lacks a definite pattern.
   

• For each of the following figures, identify the line(s) of symmetry if it exists.
  
  Sol. Below are the symmetrical figures and their lines of symmetry:
  

2. Punching Game The fold is a line of symmetry. Punch holes at different locations of a folded square sheet of paper using a punching machine and create different symmetric patterns.
   
   Sol. Do it yourself!
3. In each of the following figures, a hole was punched in a folded square sheet of paper and then the paper was unfolded. Identify the line along which the paper was folded. Figure (d) was created by punching a single hole. How was the paper folded?
   
   Sol.
   

• Given the line(s) of symmetry, find the other hole(s).
  
  Sol. Based on the symmetry given, the holes will appear as reflections across the fold line.
• Here are some questions on paper cutting. Consider a vertical fold. We represent it this way: Vertical Fold
  
  Similarly, a horizontal fold is represented as follows: Horizontal Fold
  
  Sol. Do it yourself!
• After each of the following cuts, predict the shape of the hole when the paper is opened. After you have made your prediction, make the cutouts and verify your answer.
  
  Sol. Do it yourself!
• Suppose you have to get each of these shapes with some folds and a single straight cut. How will you do it? a. The hole in the centre is a square
  
  b. The hole in the centre is a square.
  
  Sol. Do it yourself!
• How many lines of symmetry do these shapes have? i.
  
  ii. A triangle with equal sides and equal angles.
  
  iii. A hexagon with equal sides and equal angles
  
  Sol. i.
  
  ii.
  
  iii.
  
• Trace each figure and draw the lines of symmetry, if any.
  
  
  Sol.
  
• Find the lines of symmetry for the kolam below.
  
  Sol.
  
• Draw the following: a. A triangle with exactly one line of symmetry. b. A triangle with exactly three lines of symmetry. c. A triangle with no line of symmetry. It is not possible to draw a triangle with exactly two lines of symmetry? Sol.
  
• Draw the following. In each case, the figure should contain at least one curved boundary. a. A figure with exactly one line of symmetry. b. A figure with exactly two lines of symmetry. c. A figure with exactly four lines of symmetry. Sol.
  
• Copy the following on squared paper. Complete them so that the blue line is a line of symmetry. Problem (a) has been done for you.
  
  Sol.
  
• Copy the following drawing on squared paper. Complete each one of them so that the resulting figure has the two blue lines as lines of symmetry.
  
  Sol.
  
• Copy the following on a dot grid. For each figure draw two more lines to make a shape that has a line of symmetry.
  
  Sol.
  

4.0Key Features and Benefits Class 6 Maths Chapter 9 Symmetry Exercise 9.1

• Conceptual Clarity: A clear, intuitive introduction to symmetry and lines of symmetry.
• Visual Learning: Many diagrams and examples will help students visually find symmetrical figures and find their axes.
• Practical Application: Links the mathematical idea of symmetry with real-world objects and patterns to make learning more meaningful.
• Problem Solving Practice: Provides a variety of problems that allow students to practice drawing and working with lines of symmetry.
• Foundation Building: Provides a base for understanding more advanced types of symmetry (like rotational symmetry) in future exercises and grades.